A285968 Positions of 1 in A285966; complement of A285967.

2, 4, 7, 10, 12, 14, 17, 19, 22, 24, 27, 30, 32, 35, 37, 40, 42, 44, 47, 50, 52, 54, 57, 59, 62, 64, 67, 69, 71, 74, 77, 79, 82, 84, 87, 90, 92, 94, 97, 99, 102, 104, 107, 110, 112, 115, 117, 120, 122, 124, 127, 130, 132, 135, 137, 140, 143, 145, 147, 150

Offset

1,1

Comments

Conjecture: a(n)/n -> 5/2.

From Michel Dekking, Mar 15 2019: (Start)

Proof of this conjecture: it is equivalent to prove that the frequency of 1 in A285966 exists and equals 2/5.

This follows from my characterization of A285966 as a morphic sequence.

The incidence matrix of that morphism has Perron-Frobenius eigenvalue 2, with right eigenvector (1,1,2,1). It follows that the letters 2 and 4 in the fixed point of the morphism have both frequency 1/5. As these are exactly the letters that are mapped to 1 in A285966, the letter 1 has frequency 2/5 in A285966.

(End)

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

As a word, A285966 = 01010010010101001010010..., in which 1 is in positions 2,4,7,10,12,...

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* Thue-Morse, A010060 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"11" -> "1"}]
st = ToCharacterCode[w1] - 48 (* A285966 *)
Flatten[Position[st, 0]]  (* A285967 *)
Flatten[Position[st, 1]]  (* A285968 *)

Crossrefs

Cf. A010060, A285966, A285967.

Sequence in context: A288482 A177093 A164903 * A218772 A057843 A047539

Adjacent sequences: A285965 A285966 A285967 * A285969 A285970 A285971

Keyword

nonn,easy

Author

Clark Kimberling, May 06 2017

Status

approved